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Sum across sheets based on a condition

Hello; I’m trying to sum cells A1:A10 across several sheets no problem. However, if cell B1 on each of the sheets does not equal the value of 1 found on the Summary sheet, then those sheets would not be added.

In other words if Sheet3 cell B1 has a value of 2, then Sheet3 would not be included in the summing process, but Sheet2, Sheet4 through Sheet40 would be.

Keep in mind that the range A1:A10 has to show their values regardless of the value of cell B1.

How can this be done?

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